Fast Synchronization of Random Automata
Formal Languages and Automata Theory
2014-09-02 v2 Discrete Mathematics
Abstract
A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then it has a synchronizing word of size at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization by proving that with high probability, an automaton has a synchronizing word. In this article, we prove that with high probability an automaton admits a synchronizing word of length smaller than n^(1+\epsilon), and therefore that the Cerny conjecture holds with high probability.
Keywords
Cite
@article{arxiv.1404.6962,
title = {Fast Synchronization of Random Automata},
author = {Cyril Nicaud},
journal= {arXiv preprint arXiv:1404.6962},
year = {2014}
}